Universität zu Köln

Lytchak, Alexander and Wenger, Stefan ORCID: 0000-0003-3645-105X (2016). Regularity of harmonic discs in spaces with quadratic isoperimetric inequality. Calc. Var. Partial Differ. Equ., 55 (4). HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-0835

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Abstract

We study harmonic and quasi-harmonic discs in metric spaces admitting a uniformly local quadratic isoperimetric inequality for curves. The class of such metric spaces includes compact Lipschitz manifolds, metric spaces with upper or lower curvature bounds in the sense of Alexandrov, some sub-Riemannian manifolds, and many more. In this setting, we prove local Holder continuity and continuity up to the boundary of harmonic and quasi-harmonic discs.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Lytchak, Alexander UNSPECIFIED UNSPECIFIED UNSPECIFIED Wenger, Stefan UNSPECIFIED orcid.org/0000-0003-3645-105X UNSPECIFIED
URN:	urn:nbn:de:hbz:38-268175
DOI:	10.1007/s00526-016-1044-1
Journal or Publication Title:	Calc. Var. Partial Differ. Equ.
Volume:	55
Number:	4
Date:	2016
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1432-0835
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language METRIC MEASURE-SPACES; RIEMANNIAN POLYHEDRA; HIGHER INTEGRABILITY; SINGULAR SPACES; MAPS; SOBOLEV; MINIMIZERS; CURVATURE Multiple languages Mathematics, Applied; Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/26817